Pascal

Pascal was a child prodigy that became a mathematician, physicist, inventor, writer and Christian philosopher. He developed the first calculator at a very young age. He was known as the founder of modern probability theory, which is the branch of mathematics that studies the likelihood of occurrence of random events in order to predict the behavior of defined systems. For example, rolling a dice or flipping a coin. Is a random event, if you continually roll or flip the object you will get a random pattern of results. One of legendarily known statements was, “The heart has its reasons, which reason does not know.” ( pg 60) In this essay my goal is to explain what I believe the meaning is behind it. The first part of the sentence, "reason" means a cause or intention where in the second part "reason" means rationality, common sense or logical thinking. For example, say you see the most beautiful girl/boy and you don`t know this person but you fall in love with them at first sight. Your heart tells you that you love her/him even though you have no knowledge of them or about them. Your heart has its own reasons to make you fall in love, it doesn`t even care whether this person would be good to/for you, you`re in love and there is no way out. After your heart does this flutter – flutter from seeing this love of your life you may look and think realistically at the moment. You may think... THINK (you use your brain, mind, reasoning), hey, it`s stupid, I don`t know this person and I`ve fallen in love with her/him - it`s stupid-you mind tells you so. So here is the point: your heart has its own reasons-intentions (to fall in love for example) but your mind/logical thinking = reason doesn`t understand them. It doesn`t know anything about the reasons of your heart, your reason doesn`t know why you`ve fallen in love. Since your hearts feelings and brain don't speak the same language, your feelings take...

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Pascal Programming
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Pascal was designed in 1968, but was no published until the 1970 by the mind of a man named Niklaus Wirth. Niklaus Wirth was born in Winterthur, Switzerland in 1934 were he attended Swiss Federal Institute of Technology Zurich. Where he soon earns his degree in Electronic Engineering by the mid 1960’s. Pascal was named based off the memory of the late Baise Pascal, a famous French Philosopher as well as a major mathematician (Bill Catambay). This particular language was inspired by Algol along with Simula 67. Although pascal resembles Algol, It far surpasses it in run precision and capabilities. Pascal was designed to be a straight forward block Structured programming. Pascal structurally sound functionality provided the way for several new languages we use today for example, Ada, Java, Modula and so many others. Pascal was design to farther educate the development of a systematically discipline construct.
Pascal was initially designed to influence the practice of good or better program design. The language in particular is an imperative and procedural programming language (Bill Catambay). Imperative programming language simply describes the computation of each term as a statement. This important detail makes it easier to produce...

...Pascal vs Descartes Paper
Pascal’s argument is fallible because he reaches the conclusion that we should “wager” God’s existence, rather than coming up with “proof” by using deductive reasoning like Descartes provides in his argument. These early 17th century philosophers both provided writings defending the validity of the Christian religion and of God’s existence. After the Protestant Reformation of 1517, the Catholic Church’s sanctity was questioned. Different religions sprouted across Europe and citizens of Western Europe began questioning religion itself and the existence of God. Blaise Pascal and Rene Descartes each claimed to have a strong belief in Catholicism (or a denomination of), and because of this strong belief, they sought to defend the validity of the existence of God. Pascal wrote a collection of aphorisms which he started to revise into a writing he would call the “Apology of Christian Religion”. However, Pascal died before he was able to complete it. In Pascal’s Pensees (his writings were collected and organized in the 19th century and 20th century), Pascal systematically dismantles the notion that we, the people, can trust reason to validate God’s Existence. Pascal rambles on about what “we” can’t do to prove God, instead of finding his own proof of God’s existence. His approach to persuade us into believing God is to use mathematical equations and odds to reach the...

...Blaise Pascal
“There are two types of minds - the mathematical, and what might be called the intuitive. The former arrives at its views slowly, but they are firm and rigid; the latter is endowed with greater flexibility and applies itself simultaneously to the dive.” From childhood he was a scientific prodigy. Just from this quote of his you can tell that even his mind in itself can fathom things that none of us even think about on a daily basis. Blaise Pascal was born June 19, 1623 in Clermont, France. He was third born out of four children and was Etienne Pascal’s, the father, only son. But at only three years old, Blaise’s mother died, leaving the four children up to Etienne Pascal. In 1632 the Pascal family moved to Paris, France. Blaise’s father had unorthodox educational views and decided to teach his son himself. He said that Blaise was not allowed to study math or science before the age of fifteen. But of course it was impossible to keep his son’s mind away from those two subjects. At just age twelve he started to work on geometry by himself, and before long he realized that the sum of the angles of a triangle are two right angles. When his father found out about this, he gave in and allowed Blaise to have a copy of Euclid.
At age fourteen, Blaise started to attend his father’s meetings. While there he met Girard Desargues and at age fifteen came to admire his work. In June of 1639, Blaise...

...﻿Research Paper on Pascal’s Law
Blaise Pascal’s findings and contributions to the behavior of fluid in an enclosed space have been an invaluable and important concept in fluid mechanics and its applications especially in the automotive industry, mechanical engineering, and hydraulics.
Pascal's law or the principle of transmission of fluid-pressure that was proposed by Blaise Pascal. According to Bloomfield, the law is a principle in fluid mechanics that states that for a particular position within a fluid at rest, the pressure is the same in all directions.
Pascal's principle is defined as
A change in pressure at any point in an enclosed fluid at rest is transmitted undiminished to all points in the fluid
Reference List
Bloomfield, Louis (2006). How Things Work: The Physics of Everyday Life (Third Edition). John Wiley & Sons.
This principle is stated mathematically as:
is the hydrostatic pressure (given in pascals in the SI system), or the difference in pressure at two points within a fluid column, due to the weight of the fluid;
ρ is the fluid density (in kilograms per cubic meter in the SI system);
g is acceleration due to gravity (normally using the sea level acceleration due to Earth's gravity in metres per second squared);
is the height of fluid above the point of measurement, or the difference in elevation between the two points within the fluid column (in metres in SI).
The intuitive explanation of this formula is that the change in...

...Early Pascal compilers[edit]
The first Pascal compiler was designed in Zürich for the CDC 6000 series mainframe computer family. Niklaus Wirth reports that a first attempt to implement it in Fortran in 1969 was unsuccessful due to Fortran's inadequacy to express complex data structures. The second attempt was formulated in the Pascal language itself and was operational by mid-1970. Many Pascal compilers since have been similarly self-hosting, that is, the compiler is itself written in Pascal, and the compiler is usually capable of recompiling itself when new features are added to the language, or when the compiler is to be ported to a new environment. The GNU Pascal compiler is one notable exception, being written in C.
The first successful port of the CDC Pascal compiler to another mainframe was completed by Welsh and Quinn at the Queen's University of Belfast (QUB) in 1972. The target was the International Computers Limited 1900 series. This compiler in turn was the parent of the Pascal compiler for the ICS Multum minicomputer. The Multum port was developed – with a view to using Pascal as a systems programming language – by Findlay, Cupples, Cavouras and Davis, working at the Department of Computing Science in Glasgow University. It is thought that Multum Pascal, which was completed in the summer of 1973, may have been the first...

...Originally Pascal’s Triangle was developed by the Chinese of long ago. But then the French mathematician Blaise Pascal was officially the first person to discover the importance of the patterns it had within itself. But how exactly does it work??? In this research paper, I will explain how to make the Pascal’s Triangle and why it is so special.
Construction:
Pascal’s Triangle is basically a triangle of numbers. “At the tip of the triangle is the number 1, which makes up row zero. Then the second row has two 1’s by adding the 2 numbers above them to the left and right, 1 and 0 (all numbers outside the triangle are zeros). Now do the same for the second row.” 0+1= 1, 1+2=3, 2+1=3, 1+0=1. Then the results become the third row. 0+1=1, 1+3=4, 3+3=6, 3+1=4, and 1+0=1. Then the pattern continues on infinitely.
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There seems to be many patterns in this triangle. For example: The Sums of the Rows.
The Sums of the Rows:
“The sum of the numbers in any row is equal to 2 to the nth power or 2^n when n represents the number of the row.” For example:
20 = 1
21 = 1+1 = 2
22 = 1+2+1 = 4
23 = 1+3+3+1 = 8
24 = 1+4+6+4+1 = 16
Prime Numbers:
“If the 1st element in a row is a prime number (remember, the 0th element of every row is 1), all the numbers in that row (excluding the 1's) are divisible by it. For example, in row 7 (1 7 21 35 35 21 7 1) 7, 21, and 35 are all divisible by 7.”
The Hockey Stick:
“If a diagonal of numbers of any length is...

...Pascal’s Triangle is a triangular array of the binomial coefficients. The system after French mathematician Blaise Pascal. The set of numbers that form Pascal's triangle were known before Pascal. However, Pascal developed many uses of it and was the first one to organize all the information together in his treatise, Traité du triangle arithmétique (1653). The numbers originally arose from Hindu studies of combinatorics and binomial numbers and the Greeks' study of figurate numbers.
The earliest explicit depictions of a triangle of binomial coefficients occur in the 10th century in commentaries on the Chandas Shastra, an Ancient Indian book on Sanskrit prosody written by Pingala in or before the 2nd century BC.While Pingala's work only survives in fragments, the commentator Halayudha, around 975, used the triangle to explain obscure references to Meru-prastaara, the "Staircase of Mount Meru". It was also realised that the shallow diagonals of the triangle sum to the Fibonacci numbers. In 1068, four columns of the first sixteen rows were given by the mathematician Bhattotpala, who realized the combinatorial significance.
At around the same time, it was discussed in Persia (Iran) by the Persian mathematician, Al-Karaji (953–1029).It was later repeated by the Persian poet-astronomer-mathematician Omar Khayyám (1048–1131); thus the triangle is referred to as the Khayyam-Pascal triangle or Khayyam triangle in Iran....

...Blaise Pascal
Blaise Pascal was born on June 19, 1623, in Clermont, Auvergne, France. He was the third child of Étienne Pascal. He was the only male child. Blaise’s mother passed away when he was three years old. After his mother’s death, the family packed their bags up and moved to Paris. Blaise’s father, Étienne decided to teach his son. However, he did not allow Blaise to study mathematics until he was 15 years old. When Blaise was 12, he started to study geometry by himself. Blaise continued his study of geometry throughout his teenage years.
In February 1640, Blaise had his first work, Essay on Conic Sections published. He was only 17 year old at the time. Between 1642 and 1645 Blaise started to develop a digital calculator. He called this device the Pascaline.
In the year 1646, Blaise became very religious and spiritual. He then started working on some experiments dealing with atmospheric pressure. Blaise concluded that a vacuum exists. The famous mathematician Rene Descarte debated Blaise over this issue. Descarte did not believe there was a vacuum. In October 1947 Blaise wrote another book, New Experiments Concerning Vacuums. This caused a lot of debates.
After a malignant growth spread from his stomach to his brain, Blaise Pascal died on August 19, 1662 at the age of 39.
Blaise Pascal’s biggest contributions in the field of mathematics deal with probability. He and a French...